33820800 has 192 divisors, whose sum is σ = 120408960. Its totient is φ = 8294400.

The previous prime is 33820799. The next prime is 33820807. The reversal of 33820800 is 802833.

It is a tau number, because it is divible by the number of its divisors (192).

It is a super-2 number, since 2×33820800² = 2287693025280000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (24) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is not an unprimeable number, because it can be changed into a prime (33820807) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 124665 + ... + 124935.

It is an arithmetic number, because the mean of its divisors is an integer number (627130).

Almost surely, 2^33820800 is an apocalyptic number.

33820800 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 33820800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (60204480).

33820800 is an abundant number, since it is smaller than the sum of its proper divisors (86588160).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

33820800 is a wasteful number, since it uses less digits than its factorization.

33820800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 311 (or 294 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 24.

The square root of 33820800 is about 5815.5653207577. The cubic root of 33820800 is about 323.3910219335.

The spelling of 33820800 in words is "thirty-three million, eight hundred twenty thousand, eight hundred".